Since python 3.6 is no longer supported in Ubuntu 21.10 and the usual deadsnakes method also doesnt work. It gives following error.
E: The repository 'http://ppa.launchpad.net/deadsnakes/ppa/ubuntu impish Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
There is no release available in Deadsnake repo.
I was able to install using by following the steps here: https://tecadmin.net/install-python-3-6-ubuntu-linuxmint/
Step 1 – Prerequsities
sudo apt-get install build-essential checkinstall
sudo apt-get install libreadline-gplv2-dev libncursesw5-dev libssl-dev libsqlite3-dev tk-dev libgdbm-dev libc6-dev libbz2-dev
libreadline-gplv2-dev failed for me, in that case remove that and install the rest.
Step 2 – Download Python 3.6
cd /usr/src
sudo wget https://www.python.org/ftp/python/3.6.10/Python-3.6.10.tgz
sudo tar xzf Python-3.6.10.tgz
Step 3 – Compile Python Source
cd Python-3.6.10
sudo ./configure --enable-optimizations
sudo make altinstall
make altinstall is used to prevent replacing the default python binary file /usr/bin/python.
Step 4 – Check the Python Version
python3.6 -V
Thats it. You have installed python3.6 on your machine.
In case you are not able to install from there. This might help: https://askubuntu.com/questions/866901/what-can-i-do-if-a-repository-ppa-does-not-have-a-release-file/1302382#1302382